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2020 (vol. 30) - Number 3

M.A. Hammami, N.H. Rettab:

On the region of attraction of dynamical systems: Application to Lorenz equations

J. Rudy, J. Pempera, C. Smutnicki:

Improving the TSAB algorithm through parallel computing

Chiranjibe Jana, Madhumangal Pal , Guiwu Wei:

Multiple Attribute Decision Making method based on intuitionistic Dombi operators and its application in~mutual fund evaluation

S. Ogonowski, D. Bismor, Z. Ogonowski:

Control of complex dynamic nonlinear loading process for electromagnetic mill

N.A. Baleghi, M.H. Shafiei:

An observer-based controller design for nonlinear discrete-time switched systems with~time-delay and affine parametric uncertainty

Amine El Bhih, Youssef Benfatah, Mostafa Rachik:

Exact determinantions of maximal output admissible set for a class of~semilinear discrete systems

Archana Tiwari, Debanjana Bhattacharyya, K.C. Pati:

Controllabilty and stability analysis on a group associated with Black-Scholes equation

A. Sambas, I.M. Moroz, S. Vaidyanathan:

A new 4-D hyperchaotic system with no equilibrium, its multistability, offset boosting and circuit simulation

A.S.S. Abadi, P.A. Hosseinabadi, S. Mekhilef, A. Ordys:

A new strongly predefined time sliding mode controller for a class of cascade high-order nonlinear systems

ACS Abstract:

2000 (Volume 10)
Number 3/4
1. On the asymptotic stability of nonlinear discrete systems
2. Robust Possibilistic Clustering
3. Two projection-type algorithms for pseudo-monotone variational inequalities
4. Identification and suboptimal control of heat exchanger using generalized back propagation through time
5. Statistical and deterministic aspects of treatment decision making in patients with multivessel coronary artery disease
6. On the bounds on the solution of the algebraic Lyapunov and Riccati equations

On the asymptotic stability of nonlinear discrete systemsDownload full PDF article
M.Rachik, M.Lhous and A.Tridane
(Facult? des Sciences Ben M'sik, Marocco)

Discrete nonlinear systems are considered. Inspired by what was done in [2] and [6], we develop here some sufficient conditions which assure the stability of discrete-time nonlinear varying systems. The problem for discrete delayed systems is also considered.

keywords: asymptotic stability, delayed systems, discrete time-varying systems, nonlinear discrete systems, state-space technique.


Robust Possibilistic ClusteringDownload full PDF article
Jacek Łęski
(Silesian University of Technology, Poland)

Fuzzy and possibilistic clustering helps to find natural vague boundaries in data and has long been as a popular unsupervised learning method. The Fuzzy C-Means (FCM) method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantage of this method is its sensitivity to presence of noise and outliers in data. The FCM applies the constraint that the memberships of each datum across groups sum to 1. Due to this constraint and L2 norm as dissimilarity measure, the FCM has considerable trouble in noise environment. In possibilistic C-means (PCM) the above constraint is not used. In this case membership values may be interpreted as degrees of possibility that the datum belongs to the groups. In possibilistic approach still L2 norm is usually used and the second reason of sensitivity for outliers and noise remains. This paper introduces a new ε -insensitive Possibilistic C-Means (εPCM) clustering algorithm. Performance of the new clustering algorithm is experimentally compared with the PCM method using simple two-dimensional synthetic data with outliers and real-world Iris database.

keywords: fuzzy clustering, possibilistic c-means, eps-insensitivity, robust methods.


Two projection-type algorithms for pseudo-monotone variational inequalitiesDownload full PDF article
Gui-Hua Lin, Zun-Quan Xia
(Dalian University of Technology, China)

Two projection-type algorithms, different from the ones presented by Solodov & Tseng (1996) and He (1997) in the computation of stepsize, for solving pseudo-monotone variational inequality problems are presented. It is shown that the algorithms are globally convergent and, in addition, they are convergent R-linearly or Q-linearly under some mild conditions.

keywords: variational inequality, pseudo-monotone function, projection-type algorithm, error bound.


Identification and suboptimal control of heat exchanger using generalized back propagation through timeDownload full PDF article
Krzysztof Fujarewicz
(Silesian University of Technology, Poland)

This paper deals with a problem of identification and suboptimal control of a counterflow heat exchanger. From the point of view of control theory the heat exchanger is a nonlinear, multidimensional, distributed parameter, dynamical system, and due to its complexity it is difficult to identify it as a black box. In this paper a hybrid model containing neural networks is identified. Its complicated structure makes analytical calculation of gradient of performance index with respect to neural networks weights very difficult. This problem is solved using special, structural formulation of sensitivity analysis called Generalized Back Propagation Through Time (GBPTT). This method is universal - can be used for searching suboptimal parameters (weights) or suboptimal control signals in continuous or discrete in time, nonlinear, dynamical systems. Moreover, presented method is fully mnemonic. Obtained model of heat exchanger and the same methodology is used during gradient calculation of suboptimal control signal of the heat exchanger. Numerical examples are presented.

keywords: identification, nonlinear systems, distributed-parameter systems, artificial neural network.


Statistical and deterministic aspects of treatment decision making in patients with multivessel coronary artery diseaseDownload full PDF article
Piotr Walichiewicz
(Silesian School of Medicine, Poland)
Adam Mrózek and Grzegorz Drwal
(Silesian University of Technology, Poland)

Data of 137 patients with multivessel coronary artery disease were analyzed retrospectively too determine what clinical information had any relation with the selected treatment method. The deterministic analysis indicates a larger number of factors influencing the choice of treatment than the statistical analysis. Elements significant for the choice of treatment, determined both by deterministic analysis and statistical analysis: state of LAD below D1, state of D1, peripheral part of RCA, systolic function of antero-lateral segment, global left ventricular ejection fraction in angiography and echocardiography. Deterministic analysis proved that in the process of reaching the decision about choice of treatment, physicians took into consideration the results of large randomized trials, i.e. patient's age, state of left ventricular ejection fraction and state of proximal LAD segment (in this paper: state of LAD above first diagonal branch). Statistical analysis pointed only to the state of ejection fraction.

keywords: decision making, rough sets, multivessel coronary artery disease.


On the bounds on the solution of the algebraic Lyapunov and Riccati equationsDownload full PDF article
Adam Czornik and Aleksander Nawrat
(Silesian University of Technology, Poland)

Different types of bounds for solutions of continuous and discrete Lyapunov and Riccati equations obtained up to now are summarized in this paper. Some new bounds are also presented. Efficiency of each bound is illustrated with three numerical examples. A discussion and comparison are given as well. The results may be particularly convenient to get the ready estimate of the solution while solving the equations numerically or to develop theoretical results that rely on these bounds.

keywords: Riccati equations, Lyapunov equations, eigenvalues bounds.


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